An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Fri Jul 18 13:24:49 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM (in Magma)
BASIS (in Magma; to be divided by square root of 3)
MINIMAL_NORM
PROPERTIES
COMMENTS
NOTES
LAST_LINE

• NAME
  P60q
  

• DIMENSION
  60
  

• DET
  1
  

• GRAM (in Magma)
  G60:=MatrixAlgebra(IntegerRing(), 60) ! \[ 6, -2, 1, 0, -1, 0, 0, -1, 1, -1, 1, 2, 0, 0, 0, 2, -1, -1, 3, 0, 1, 0, -1, -1, 1,
  0, -1, 1, 1, -1, -1, 1, -1, 1, 2, -1, -2, -1, 1, -1, 1, 0, 1, -3, 1, 1, -2, 1, 1, 0, 0, 1, 0, -1, 2, 0, 0, -1, 0, -1, -2,
  6, -1, 2, 0, -1, 0, 0, 1, 0, 0, -1, -1, 1, -2, 0, 2, 2, -1, 0, 2, 0, 0, -1, 1, -1, 0, 1, -2, 1, 0, 1, 0, -1, -1, 1, 1, -1,
  1, -1, 0, 0, 0, 1, -1, -1, 0, -1, 0, 2, 1, 0, 2, 0, -1, 1, 1, 0, 0, 1, 1, -1, 6, -1, 3, -2, -3, -1, -3, 2, -3, 0, 3, 0, 3,
  3, -3, 0, 2, -1, -3, -1, -3, 3, 3, -1, 3, 0, 3, 0, -1, -2, 0, 3, 0, -3, 0, -1, 1, 2, -2, 3, -3, 2, -2, 3, -2, 1, 3, -2,
  -3, 2, -2, 2, 3, 1, 3, -3, 1, -3, 0, 2, -1, 6, 0, 0, 2, 2, 1, 0, 2, 2, -1, 1, -2, 0, 1, 1, 0, -1, 2, -1, -1, 0, 0, 0, 0,
  0, -2, 1, -2, 0, 0, -1, -2, 1, -1, -1, 1, -1, 1, -1, 2, -1, -1, 0, 1, 1, -2, 2, 1, 0, 0, 1, 0, -1, 2, -1, 2, -1, -1, 0, 3,
  0, 6, -2, -3, -1, -3, 1, -3, 0, 3, -1, 3, 0, -3, 1, 1, 1, -3, -2, 0, 3, 0, 0, 3, -2, 0, 1, -1, 0, 2, 0, -1, -3, 1, -2, 3,
  0, -2, 0, -2, 2, 0, 1, 1, -1, 0, 1, -2, 1, -2, 2, 1, 3, 3, -1, 2, -3, 0, -1, -2, 0, -2, 6, 2, 1, 1, -1, 0, 0, -2, 0, -1,
  -1, 1, 1, -1, 1, 1, 0, 1, -2, -2, 1, 0, -1, 0, -2, 0, 0, -1, 0, 1, 0, 1, 0, -2, -1, 1, -1, 2, -2, 2, 0, -1, -1, -2, 0, 2,
  0, 1, -1, -1, 0, -3, 1, 1, 2, 0, 0, -3, 2, -3, 2, 6, 1, 3, -2, 3, 1, -3, 2, -3, 0, 3, 0, -1, 0, 3, 0, 0, -3, 0, 1, -3, 0,
  -3, -1, 0, 1, -1, 0, -1, 3, -1, 1, -1, 1, 0, -3, 3, -2, -1, -2, 0, 1, -2, -1, 2, 0, 0, 0, -1, -3, -1, 2, 0, 2, -1, 0, -1,
  2, -1, 1, 1, 6, -1, 0, 0, 1, 0, 0, 0, -1, -1, -1, -1, -1, 0, 1, 1, 1, -2, 2, 1, 0, 1, 0, 0, 0, 0, -2, -1, 1, -1, 2, -1,
  -1, 2, 1, 1, 0, -1, 0, 1, 1, -1, 0, -1, 1, -1, -1, -1, -1, -2, 0, 1, -1, 1, 1, -3, 1, -3, 1, 3, -1, 6, -2, 3, 1, -3, 0,
  -3, 0, 3, 1, 0, 1, 3, 0, 0, -3, 0, -1, -3, 1, -3, 1, 1, 2, 0, 0, -1, 3, 0, -1, -1, -1, 1, -3, 3, -2, 1, -1, 1, -1, 0, 1,
  2, 0, 0, -1, -1, -1, 0, 3, 0, 4, -1, 0, 2, 0, 1, -1, -2, 0, -2, 6, -2, 0, 1, 0, 1, 2, -1, -1, 0, 1, -1, 0, -2, 2, 2, 0, 1,
  -1, 1, 0, -2, -2, -1, 2, 1, -1, -1, 1, 1, 1, 0, 2, -1, 2, 1, 3, 1, 2, 1, 1, -2, -1, -1, 2, 2, -1, 1, -2, 2, -2, 1, 0, -3,
  2, -3, 0, 3, 0, 3, -2, 6, 1, -3, 2, -3, 0, 3, -1, -1, -1, 3, 2, 0, -3, 0, 0, -3, 2, -3, 0, 0, 2, 0, 0, -1, 3, 0, 1, -2, 1,
  2, -2, 2, -3, -1, -2, 1, 0, -1, -1, 3, 0, 0, -2, -2, -3, -1, 2, -2, 2, 2, -1, 0, 2, 0, 0, 1, 1, 1, 0, 1, 6, 1, 0, -1, 0,
  -1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, 2, -1, 1, 0, 1, -1, -1, 1, -2, 1, -1,
  0, 0, 0, 2, 1, 0, 0, 0, -1, 3, -1, 3, -2, -3, 0, -3, 1, -3, 1, 6, -1, 3, 0, -3, 0, 0, -1, -3, -1, 0, 3, 0, 1, 3, 0, 3, 0,
  1, 0, 1, 0, 0, -3, 0, -1, 2, 1, -2, 1, -2, 3, 0, 0, 1, -1, 2, -1, -3, 2, -1, 2, 2, 2, 2, -1, -1, -2, 0, 1, 0, 1, -1, 0, 2,
  0, 0, 0, 2, 0, -1, 6, 0, 1, 1, 0, 0, 0, 2, 1, -2, -1, 1, 1, -1, 2, -1, -2, -1, 1, -1, 1, -1, 0, 0, 2, -1, 3, -1, 1, -1, 0,
  -3, 0, 0, 0, 0, -1, 0, 1, -1, 1, 0, -2, 0, 0, -1, 0, 0, -2, 3, -2, 3, -1, -3, 0, -3, 1, -3, -1, 3, 0, 6, 0, -3, 0, 2, 1,
  -3, -1, 0, 3, 0, 0, 3, 0, 3, -1, -1, 0, 0, 0, -1, -3, 0, 0, 0, 1, -1, 2, -3, 3, -1, 2, 1, 0, 1, 0, -3, 2, -2, 2, 0, 1, 1,
  -2, 0, -3, 2, 0, 3, 0, 0, -1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 6, 0, -1, 1, 0, 0, 0, -3, 0, 3, -1, 0, 1, 0, -1, -2, -1, -1, 3,
  0, 0, -1, -1, 0, 2, 0, 1, -1, 0, -2, 3, -2, 2, 2, -2, -1, 1, -2, 1, 2, -2, 2, -2, 1, -1, -1, 2, -3, 1, -3, 1, 3, -1, 3,
  -1, 3, -1, -3, 1, -3, 0, 6, 0, -1, -1, 3, 1, 0, -3, 0, 0, -3, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 1, -1, 1, 1, -2, 2, -2, -1,
  -2, 0, 0, -1, -1, 3, -1, 2, -1, -2, -3, -1, 1, -1, 3, -1, 2, 0, 1, 1, 1, 0, -1, 1, -1, -1, 0, 0, 0, 0, -1, 0, 6, 1, 2, 1,
  -2, 1, 0, 0, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 0, 2, -2, -1, -2, -1, -1, 1, 0, 0, -1, 0, -1, -1, 1, 0, 1, 1, 2, 0, 1, 2,
  1, 1, 1, 3, -1, 2, 0, 1, -1, -1, -1, 0, 0, -1, 0, 0, 0, 2, 1, -1, 1, 6, 1, 0, -3, -2, 1, 1, 0, 0, 0, 1, 1, -2, 0, -1, 1,
  1, -1, -2, -1, 1, -1, 0, 1, 0, -1, -1, 1, -1, 1, 0, 1, -1, 0, -1, 1, 1, -1, 2, -2, 1, -2, 0, 0, -1, -1, 1, 1, 0, -1, 1, 1,
  -1, 0, -1, 0, 1, 0, -1, 2, 1, 6, 0, -1, 2, 0, 0, 0, 0, -2, -1, 0, -1, 2, -1, 0, 0, -1, 1, -1, 0, -1, 0, 0, 2, 0, 3, 1, 1,
  0, -1, 3, 0, -1, -1, 0, 0, 1, 0, 1, 1, 0, 1, 2, -3, 2, -3, 1, 3, 0, 3, -1, 3, 1, -3, 2, -3, 0, 3, 1, 0, 0, 6, 0, 0, -3, 0,
  1, -3, 2, -3, -1, -1, 2, -2, 0, 1, 3, -1, 1, -2, -1, 3, -3, 2, -3, -1, -2, 0, -1, -2, 1, 0, 1, 1, 1, 0, -2, -1, 3, -1, 3,
  0, 0, -1, -1, -2, 0, 0, 1, 0, 0, 2, 0, -1, 1, -1, 0, 1, -2, -3, -1, 0, 6, 1, -1, 0, 0, 0, 1, 0, -1, 1, 1, 0, 0, 0, 1, 1,
  2, -1, 1, 1, 1, 0, -1, 0, 0, 0, 1, 1, -1, 1, 0, 1, -3, -1, 0, -2, 0, -2, 1, -1, 0, -3, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, -2,
  0, -3, 0, 1, -2, 2, 0, 1, 6, 0, -3, 0, 0, -1, 0, 0, 1, 2, 1, -3, 0, 0, 1, 0, -1, -3, 2, -1, 2, -1, 3, -3, 1, 0, -1, 1, 1,
  0, 1, -2, -2, 2, -3, 2, -2, 0, -1, -1, 3, 0, 3, -2, -3, 1, -3, 2, -3, 0, 3, -1, 3, 0, -3, 0, 1, 0, -3, -1, 0, 6, 0, 0, 3,
  -1, 3, 1, -1, -2, 1, 0, -1, -3, -1, 0, 1, 0, 0, 2, -2, 2, -1, 1, 1, 1, 0, 0, -3, 0, -2, 2, 0, 2, 2, -3, 1, -2, 1, 1, 3, 0,
  0, -2, 0, -2, 0, 2, 0, 1, 0, 1, 0, 3, 0, 0, 1, 0, 0, 0, -3, 0, 6, -2, 0, 1, 0, 1, -1, 0, -1, 3, 0, 0, 0, -1, 1, 2, -2, 1,
  0, 1, -1, 2, -2, 1, 1, -1, -1, 0, -1, 1, 1, -1, 3, -2, 0, 0, 0, -1, -1, 0, 0, 1, 1, 2, -1, 0, 0, 2, 1, 1, 0, -1, 0, -1, 0,
  0, 1, 0, 0, 0, -2, 6, 1, -1, 0, -1, 0, 1, -1, 0, 1, 0, -1, 2, -1, 1, 1, -1, 0, 0, -1, -1, 2, -2, -2, 0, -2, 1, 1, 0, 0,
  -1, -1, 2, 0, 1, -1, 0, 3, 0, 3, 0, -3, 1, -3, 1, -3, 1, 3, -1, 3, 0, -3, 1, 0, 0, -3, 0, 0, 3, 0, 1, 6, -2, 3, 0, 0, 0,
  0, 0, -1, -3, 1, -1, 0, 0, -1, 2, -2, 3, -1, 2, 1, -1, 0, 1, -3, 2, 0, 0, 0, 2, 2, -2, 1, -2, 1, 1, 0, 0, -2, -1, 0, 0, 1,
  -1, 2, 0, 0, 2, 0, 1, 1, -1, 0, -2, 2, 1, -1, -1, 1, -1, -2, 6, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 1, 1, 0, -1, -1, -2, 0,
  -1, 0, 2, -1, 0, 1, -1, 0, 0, -1, 0, 0, -3, 1, 1, -2, 3, -2, 0, 0, -3, 1, -3, 1, -3, 0, 3, -1, 3, 0, -3, -1, 1, -1, -3, 0,
  0, 3, 0, 0, 3, 0, 6, -1, 1, -2, 0, 0, 1, -3, -1, 1, -1, 0, 0, 4, -2, 2, 0, 1, -1, 1, 2, -1, -2, 1, 0, 0, 1, 1, -1, -3, -1,
  -3, -1, 1, 0, 1, 1, -2, -1, 0, 1, 0, 0, 0, 0, -2, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, -1, 0, -1, -1, 6, 0, 0, 1, 0, -1,
  1, 1, -1, 2, -1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 1, 2, 0, 1, 1, -1, 0, -1, -2, -1, 0, 0, 0, 1, -2, 0, 0, 1,
  -1, -1, -2, 0, -1, -2, -1, -1, 1, 1, -1, -1, 0, 0, 0, 1, 0, 6, 1, 2, -2, 0, 0, 1, 0, 0, 0, -2, 0, 1, 1, 1, -2, 1, -3, 1,
  0, 1, 0, 0, -2, -1, 1, -2, 2, -2, 1, 1, 1, -2, 0, 0, 0, 1, 0, 2, -2, 2, 2, 0, 1, 0, -1, 0, 1, 0, 2, 2, 1, 2, -2, 0, 1, 0,
  1, -2, 0, 1, 6, 0, -1, -1, 1, 1, -1, 0, -1, 0, -2, 2, -1, 1, -2, 2, -2, -1, 2, 0, 2, -1, -1, -1, 1, 0, 3, -2, 1, -1, 0, 0,
  0, 2, -1, -1, 0, 0, -1, 0, 0, 1, -1, 0, -1, 0, -1, -1, -1, -2, 0, 1, 1, -1, -1, 0, 0, 0, 1, 2, 0, 6, -2, -2, 0, 0, -1, 1,
  -1, -1, 0, 1, 0, 1, -1, 1, -1, 0, 0, 2, 0, -2, -1, -1, 1, -1, 0, 1, -2, 1, -1, 3, -1, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, 3,
  0, 1, 1, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, -2, -1, -2, 6, 1, 0, 1, 0, -1, 3, -1, 0, -2, 0, -1, 1, -1, 1, 1, -3, -1, 1, 0,
  2, 3, -1, 2, 0, 1, 1, 2, -1, 0, -2, -1, 1, -1, -1, -1, 1, -1, 0, 0, -1, -1, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, 1, -1, 0, 1,
  -1, 0, -1, -2, 1, 6, -1, 0, 1, 1, 0, 1, 0, 0, -2, 2, 0, -2, 0, 0, 0, -1, -1, 2, -1, 2, 0, -1, 0, -1, 1, -1, 1, -3, 1, -3,
  0, 3, 1, 3, -1, 3, 0, -3, 0, -3, 0, 3, 0, -1, -1, 3, 1, 0, -3, 0, 0, -3, 1, -3, 1, 0, 1, 0, 0, -1, 6, -1, 1, -2, -1, 2,
  -2, 2, -1, -1, -2, 0, 1, -1, -1, 1, 0, 0, 0, -1, -3, -1, 2, 0, 2, -2, 1, 0, -1, 1, 1, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1,
  0, 2, -2, 1, -1, 1, 1, -1, 0, -1, 1, 0, -1, 1, 1, 1, 0, 1, 0, -1, 6, -1, 0, 2, -2, 0, -1, 1, 1, 0, 0, -2, 0, 0, 1, 0, 1,
  -1, 0, 2, 1, 2, -1, 2, -1, -1, -1, -1, -2, 0, 1, 2, -1, 1, 1, -1, -1, 2, 0, -1, 1, -2, -1, -1, 1, 2, 0, 0, -1, 2, -1, 0,
  1, -1, 0, -1, -1, 0, 1, 1, -1, 7, -2, 2, 2, 1, -1, 0, -2, -1, 1, 1, 0, -2, -1, 1, 0, 0, 0, -2, -3, 1, -2, 0, 1, 1, 1, 1,
  3, -2, -1, -1, -1, 1, -2, 0, 2, -1, 0, 0, -1, -1, 1, 0, -2, -1, -1, 1, 1, -1, 0, -1, -1, 2, 0, 0, 1, -1, 1, -2, 0, -2, 8,
  0, -3, 0, 0, 1, 2, 1, -1, 1, 1, 2, 0, -2, 0, 0, 2, 3, 3, -3, 1, -2, -1, -1, 2, -1, 0, -1, 1, -1, -1, 1, 1, -1, 1, 3, 1, 2,
  1, -2, -1, -1, -1, 1, -3, 0, 2, 1, 0, 1, 0, -1, 0, -1, -1, 3, 0, -1, 2, 2, 0, 8, -2, 1, -3, 2, -3, 1, 0, 0, 1, -3, -1, 1,
  -1, 1, 1, -2, 2, 0, -1, 1, 1, 0, -2, 1, -2, 1, 0, 2, 1, 0, 2, 0, -2, -1, -1, 0, 1, -1, 0, 0, 3, 1, 2, 0, -2, 1, -1, 1, 0,
  0, -2, 0, -1, -1, 1, 2, -2, 2, -3, -2, 8, -1, 1, -2, 0, -1, 0, 1, 0, 0, -1, 2, 0, -1, -1, -1, -3, 1, -1, 1, 0, 0, 3, -1,
  0, -1, -3, 1, -3, 2, -2, -1, 1, 1, 2, 1, -2, -1, 1, 0, -3, 1, -1, 2, 1, -1, 2, 0, 4, 0, 0, -2, 0, 0, 0, -2, 0, 1, 0, 1,
  -1, 8, -2, 2, 0, 3, -3, 2, 3, 0, -1, -1, 0, -1, 1, 1, 0, -4, 0, -4, 1, 0, -3, 2, -2, 2, 3, 1, 3, -1, 2, 2, -2, -1, -3, -1,
  2, 1, 0, 2, 2, 0, 2, -2, 0, 0, -2, -1, -2, 1, 1, 2, 1, -2, 0, 2, -1, -1, 0, -3, 1, -2, 8, -4, 3, -1, 0, 1, -2, 2, 3, -1,
  -1, -2, -1, -2, -2, 1, 1, 1, -3, 1, 2, -1, 2, -2, -2, 0, -2, 2, -3, -1, 3, 0, 3, 0, -2, 0, -1, 0, -3, -1, -1, 2, 1, 0, 3,
  -1, 2, 1, 1, -1, 0, 0, -2, -1, 1, 0, 1, 2, -2, 2, -4, 8, -1, 1, 2, -1, 2, 0, -3, 1, 0, 2, 0, 1, 2, -1, 0, -2, 1, -1, -2,
  -1, 0, 2, -1, -1, 1, 1, -1, 1, 0, -3, -1, -2, -1, 0, -1, 3, -1, 0, 3, -1, -1, -1, -1, -2, 0, 1, 1, 1, 1, -1, 2, -1, 1, -2,
  2, -3, 0, 0, 3, -1, 8, 0, 0, 0, 0, 3, 2, -3, 1, -2, 1, 3, -2, 1, 1, 0, 1, -1, 3, 0, 1, 0, -2, 0, -1, 3, -2, 0, 0, 0, 2, 3,
  -2, -1, 1, 1, -2, 0, -3, 1, 2, -1, 2, 0, 1, 0, -2, -2, -1, 1, 0, -2, 0, -1, 1, 1, -1, 3, -1, 1, 0, 8, -2, 1, 2, 2, -2, -1,
  -1, -1, 2, 0, 2, -3, 3, -1, -2, 0, -2, 1, 1, -1, 0, 1, 1, 1, 1, 1, 1, 0, 1, -2, 0, 0, -1, 1, 0, 0, 1, 1, -2, 2, 1, -1, -1,
  0, 1, 2, 1, -1, -2, 0, 0, 1, -1, 0, 0, -3, 0, 2, 0, -2, 8, -2, -2, 2, 0, 1, -1, 1, -2, -1, 0, 3, 0, 0, 1, -1, 1, 1, -1,
  -1, 1, 1, -1, 2, 0, -1, -1, 0, 0, 2, 0, -1, 1, 0, -1, 1, 0, 1, 1, -2, -1, 0, 1, 0, -3, -2, -1, 1, 0, 1, -2, 1, 1, 0, 1, 2,
  1, -1, 0, 1, -2, 8, 2, -1, 1, -1, -1, 0, 2, -2, 0, -4, 1, -4, 1, 0, 3, -2, 0, -2, -2, -1, 0, 1, -1, -1, 2, 0, 1, 2, -1,
  -1, 0, -1, -2, 1, -1, 0, 1, -2, 0, 2, 2, 0, 1, -1, 0, 1, 0, -1, 0, 0, 1, 1, 0, 3, -2, 2, 0, 2, -2, 2, 8, -2, -1, 2, -1,
  -1, 3, 1, 0, -1, -2, -2, 0, 2, -2, 2, 1, 0, -1, 0, 1, 1, -1, 1, -1, -1, 0, -2, -1, 1, 1, 3, 1, -1, 1, 0, -1, 0, 1, -1, -1,
  1, 0, 2, 0, -3, 0, -1, 0, -2, 2, -3, 0, 0, 2, 0, 3, 2, 2, -1, -2, 8, 0, -2, 1, -1, 0, 2, 1, 0, 2, -1, 0, 1, -3, 1, -2, 2,
  2, -1, 2, -2, 3, -2, -3, 0, -3, -1, 3, 0, -1, 0, 0, 1, 1, -3, -1, -2, -3, 0, -2, 0, 1, 0, 2, -1, -1, 1, 1, -1, 0, -1, -1,
  -1, 3, -3, 2, -2, 0, 1, -1, 0, 8, -3, 2, -3, -2, -1, -3, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, -1, 0, 1, 2, 1, 2, 1, -1, 1,
  0, -1, 1, 0, 0, 0, 0, 1, 2, 1, 1, -2, 0, 2, 0, 1, -1, 0, 0, 1, -2, 1, 2, -1, -1, 1, -3, -1, 1, -1, 2, -2, -3, 8, -2, 2, 1,
  0, 0, 2, -1, -1, 0, 2, -2, 0, -2, 1, 0, -1, 0, -1, 0, -1, -1, -1, -2, -2, 2, 1, -1, -1, 1, 1, 1, -2, -1, 1, 0, -1, 0, 0,
  0, -1, -2, 0, 2, 0, 1, 0, 0, -1, 0, 0, -1, 0, 1, -1, -1, -1, -1, 1, 2, -2, 8, -2, 0, 1, -1, 0, -1, 2, -1, 0, 2, 1, 2, -1,
  0, -1, -1, 2, -2, 0, 2, 1, 2, 1, -1, 2, 1, 0, 1, -3, -2, 2, 1, 0, 0, 0, 0, -1, -2, -1, -1, 2, -1, 0, -1, 0, 0, 1, -1, -1,
  -2, 2, -2, -1, 1, 0, -1, -1, -3, 2, -2, 8, 2, 0, 3, 0, 1, -1, 2, -1, 3, 0, 1, -1, -1, -1, -1, 2, -2, 0, 2, 0, 0, 2, -2, 0,
  1, 0, 0, -1, -2, 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 3, 2, -1, 0, 0, 2, 1, -1, 1, -1, 0, 1, 2, -2, 2, 3, 0, -2, 1, 0, 2, 8,
  1, 1, 0, 1, -2, 0, 1, 1, -1, 3, 0, -3, -1, -1, -1, -3, 0, 2, -2, 1, -2, -3, 1, -1, 1, -2, 0, 2, 2, -1, -1, 2, -1, 1, 1, 1,
  1, 1, -1, 0, -3, 2, -2, 3, -2, -1, 1, -2, 1, 3, 0, -1, -2, 1, 2, -1, 0, 1, 0, 1, 8, 1, 0, 0, 0, 0, 1, 3, 2, 3, -3, -1, -2,
  0, 1, -1, 2, 2, 0, 1, 2, -1, 2, 2, 0, -1, -2, -3, 2, 3, -1, 2, 0, -1, 2, -2, 0, -1, 2, -1, -1, 1, -3, 3, 2, -3, 0, -2, 2,
  -2, 2, 0, 0, 0, 1, -3, 0, -1, 3, 1, 1, 8, -2, 1, 0, -1, 0, -3, -1, -1, 1, 2, 0, 3, -2, 2, 1, -1, 0, -2, -2, 1, 1, -2, 1,
  3, 0, 2, -3, -2, 2, -2, 0, -3, 0, 2, 3, 0, 0, 0, 2, 2, 1, -3, 0, 1, -4, 1, -1, 1, -3, 3, -4, -1, 0, 0, 2, 0, 0, 0, 0, -2,
  8, -1, 4, 0, 0, 1, 2, 2, 1, 0, 1, 0, 2, -2, 0, -1, -1, 0, 1, -1, 1, 1, 1, -1, -2, -2, 1, 0, 0, 1, -3, -1, 1, -2, -2, 1, 1,
  -1, 0, -1, -2, 1, -1, -1, 0, 1, 0, 1, 3, 0, 1, -2, 2, 0, -1, -1, 1, 1, 0, 1, -1, 9, -1, -1, 1, -3, -1, -3, 2, 2, -1, 4,
  -2, 2, 0, -2, 0, -3, -1, 3, 1, -2, 0, 3, 1, 0, -2, 0, 1, -2, 1, -3, 1, 1, 1, -2, 1, 1, 2, 2, 0, -2, 1, 1, -4, 1, -2, 0,
  -1, 0, -4, -2, -1, 0, -1, 2, -1, -2, 0, 0, 4, -1, 10 ];
  

• BASIS (in Magma; to be divided by square root of 3)
  B60:=KMatrixSpace(RationalField(), 119, 60) ! [ -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1,
  1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1,
  -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1,
  1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1,
  -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1,
  1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1,
  -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1,
  1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1,
  -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1,
  -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1,
  1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1,
  -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1,
  -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1,
  1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1,
  1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1,
  -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1,
  1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1,
  -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1,
  -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1,
  -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1,
  -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1,
  -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1,
  1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1,
  1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1,
  1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1,
  -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1,
  -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1,
  -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1,
  -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1,
  -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1,
  1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1,
  -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1,
  -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1,
  1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1,
  1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1,
  1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
  1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1,
  -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1,
  -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1,
  1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1,
  1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1,
  -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1,
  1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1,
  -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1,
  -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1,
  1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1,
  1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1,
  1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
  1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1,
  -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1,
  1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1,
  1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1,
  1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
  1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1,
  -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1,
  1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1,
  1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1,
  -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
  1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1,
  -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,
  -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1,
  1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1,
  1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1,
  -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
  1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1,
  -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1,
  1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,
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  0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,
  0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0,
  3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -5/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2,
  1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2,
  1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2 ];
  

• MINIMAL_NORM
  6
  

• PROPERTIES
  UNIMODULAR = 1
  EXTREMAL = 1
  

• COMMENTS
  Date: Wed, 27 Jun 2001 00:15:09 +0200 (MET DST)
  From: gaborit@unilim.fr (Philippe Gaborit)
  Here is an extremal unimodular lattice P60q that I found in Nov 2000.
  The construction is the same as that used for
  the lattice P48q, adapted to the extended quadratic residue
  code of length 59 over F3. The result relies on the computation of the complete
  weight enumerator of XQ59, which is different from the complete weight enumerator of PS(60)
  computed in the paper by Mallows, Pless and Sloane, "Self-Dual Codes over GF(3)".
  This computation shows that the words of weight
  60 of XQ59 only contains even numbers of 1 or -1,
  which implies that one can apply the construction described in SPLAG p.149.
  Adding one vector (-5/2,(1/2)^59) to hP60q one obtains an unimodular lattice of min 6.
  Of course the automorphism group of the lattice contains
  (as for P48q) the group SL2(59). I couldn't yet prove it was exactly this group.
  This will be a part of a forthcoming paper "Construction of extremal unimodular lattices with
  self-dual codes".
  

• NOTES
  Probably equivalent to the lattice HKO60.
  

• LAST_LINE
  
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe